To sow more confusion :)
rxvt isn't a shell - it's a terminal emulator, specifically meant to emulate the DEC vt100 series physical terminal. The
-e /bin/bash in the accepted answer is what kicks off your shell (bash in this case), passing bash
--login to make it a login shell.
2) Besides rxvt you may want to try mintty. I find it more modern, and cleaner. It's a more native Windows style app, with Windows cut and paste rules. I like it better, YMMV. I have no Cygwin install in front of me to test this, but
C:\cygwin\bin\mintty.exe -e /bin/bash --login should work
3) Also look at the
chere command line app, which adds the registry entries to say 'start shell here' to your explorer windows. It allows you to say which terminal emulator to use.